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Volumn 143, Issue 1, 2006, Pages 124-133

Continuous and discrete least-squares approximation by radial basis functions on spheres

Author keywords

Error estimates; Norming sets; Radial basis functions; Scattered data

Indexed keywords


EID: 33750358239     PISSN: 00219045     EISSN: 10960430     Source Type: Journal    
DOI: 10.1016/j.jat.2006.03.007     Document Type: Article
Times cited : (57)

References (22)
  • 1
    • 5844297152 scopus 로고
    • Theory of reproducing kernels
    • Aronszajn N. Theory of reproducing kernels. Trans. Amer. Math. Soc. 68 (1950) 337-404
    • (1950) Trans. Amer. Math. Soc. , vol.68 , pp. 337-404
    • Aronszajn, N.1
  • 3
    • 0042507795 scopus 로고
    • Adaptive least squares fitting with radial basis functions on the sphere
    • Dæhlen M., Lyche T., and Schumaker L.L. (Eds), Vanderbilt University Press, Nashville
    • Fasshauer G.E. Adaptive least squares fitting with radial basis functions on the sphere. In: Dæhlen M., Lyche T., and Schumaker L.L. (Eds). Mathematical Methods for Curves and Surfaces (1995), Vanderbilt University Press, Nashville 141-150
    • (1995) Mathematical Methods for Curves and Surfaces , pp. 141-150
    • Fasshauer, G.E.1
  • 4
    • 0000669521 scopus 로고    scopus 로고
    • Scattered data fitting on the sphere
    • Dæhlen M., Lyche T., and Schumaker L.L. (Eds), Vanderbilt University Press, Nashville
    • Fasshauer G.E., and Schumaker L.L. Scattered data fitting on the sphere. In: Dæhlen M., Lyche T., and Schumaker L.L. (Eds). Mathematical Methods for Curves and Surfaces II (1998), Vanderbilt University Press, Nashville 117-166
    • (1998) Mathematical Methods for Curves and Surfaces II , pp. 117-166
    • Fasshauer, G.E.1    Schumaker, L.L.2
  • 7
    • 0035529218 scopus 로고    scopus 로고
    • Interpolation by polynomials and radial basis functions on spheres
    • Golitschek M.v., and Light W.A. Interpolation by polynomials and radial basis functions on spheres. Constr. Approx. 17 (2001) 1-18
    • (2001) Constr. Approx. , vol.17 , pp. 1-18
    • Golitschek, M.v.1    Light, W.A.2
  • 8
    • 3042730696 scopus 로고    scopus 로고
    • A Duchon framework for the sphere
    • Hubbert S., and Morton T.M. A Duchon framework for the sphere. J. Approx. Theory 129 (2004) 28-57
    • (2004) J. Approx. Theory , vol.129 , pp. 28-57
    • Hubbert, S.1    Morton, T.M.2
  • 9
    • 3042855065 scopus 로고    scopus 로고
    • p-error estimates for radial basis function interpolation on the sphere
    • p-error estimates for radial basis function interpolation on the sphere. J. Approx. Theory 129 (2004) 58-77
    • (2004) J. Approx. Theory , vol.129 , pp. 58-77
    • Hubbert, S.1    Morton, T.M.2
  • 10
    • 33745756430 scopus 로고    scopus 로고
    • On the accuracy of surface spline interpolation on the unit sphere
    • Neamtu M., and Saff E.B. (Eds), Nashboro Press, Brentwood, TN
    • Hubbert S., and Morton T.M. On the accuracy of surface spline interpolation on the unit sphere. In: Neamtu M., and Saff E.B. (Eds). Advances in constructive approximation: Vanderbilt 2003 (2004), Nashboro Press, Brentwood, TN 227-242
    • (2004) Advances in constructive approximation: Vanderbilt 2003 , pp. 227-242
    • Hubbert, S.1    Morton, T.M.2
  • 11
    • 33750349298 scopus 로고    scopus 로고
    • Norming sets and scattered data approximation on spheres
    • Chui C.K., and Schumaker L.L. (Eds), Vanderbilt University Press, Nashville
    • Jetter K., Stöckler J., and Ward J.D. Norming sets and scattered data approximation on spheres. In: Chui C.K., and Schumaker L.L. (Eds). Approximation Theory IX, vol. 2: Computational Aspects (1998), Vanderbilt University Press, Nashville 137-144
    • (1998) Approximation Theory IX, vol. 2: Computational Aspects , pp. 137-144
    • Jetter, K.1    Stöckler, J.2    Ward, J.D.3
  • 12
    • 84942296295 scopus 로고    scopus 로고
    • Improved error bounds for solving pseudodifferential equations on spheres with zonal kernels
    • Kopotun K., Lyche T., and Neamtu M. (Eds), Vanderbilt University Press, Nashville
    • Morton T.M. Improved error bounds for solving pseudodifferential equations on spheres with zonal kernels. In: Kopotun K., Lyche T., and Neamtu M. (Eds). Trends in Approximation Theory (2001), Vanderbilt University Press, Nashville 317-326
    • (2001) Trends in Approximation Theory , pp. 317-326
    • Morton, T.M.1
  • 13
    • 0036186647 scopus 로고    scopus 로고
    • Error bounds for solving pseudodifferential equations on spheres by collocation with zonal kernels
    • Morton T.M., and Neamtu M. Error bounds for solving pseudodifferential equations on spheres by collocation with zonal kernels. J. Approx. Theory 114 (2002) 242-268
    • (2002) J. Approx. Theory , vol.114 , pp. 242-268
    • Morton, T.M.1    Neamtu, M.2
  • 14
    • 0242360744 scopus 로고    scopus 로고
    • Refined error estimates for radial basis function interpolation
    • Narcowich F.J., Ward J.D., and Wendland H. Refined error estimates for radial basis function interpolation. Constr. Approx. 19 (2003) 541-564
    • (2003) Constr. Approx. , vol.19 , pp. 541-564
    • Narcowich, F.J.1    Ward, J.D.2    Wendland, H.3
  • 15
    • 14944361055 scopus 로고    scopus 로고
    • Sobolev bounds on functions with scattered zeros, with applications to radial basis function surface fitting
    • Narcowich F.J., Ward J.D., and Wendland H. Sobolev bounds on functions with scattered zeros, with applications to radial basis function surface fitting. Math. Comput. 74 (2005) 743-763
    • (2005) Math. Comput. , vol.74 , pp. 743-763
    • Narcowich, F.J.1    Ward, J.D.2    Wendland, H.3
  • 16
    • 33745292987 scopus 로고    scopus 로고
    • F.J. Narcowich, J.D. Ward, H. Wendland, Sobolev error estimates and a Bernstein inequality for scattered data interpolation via radial basis functions, Constr. Approx., in press, doi:10.1007/s00365-005-0624-7 (Published online 12 April 2006).
  • 17
    • 0001878701 scopus 로고
    • Positive definite functions on spheres
    • Schoenberg I.J. Positive definite functions on spheres. Duke Math. J. 9 (1942) 96-108
    • (1942) Duke Math. J. , vol.9 , pp. 96-108
    • Schoenberg, I.J.1
  • 18
    • 0000384573 scopus 로고
    • Spaces of Besov-Hardy-Sobolev type on complete Riemannian manifolds
    • Triebel H. Spaces of Besov-Hardy-Sobolev type on complete Riemannian manifolds. Ark. Mat. 24 (1986) 299-337
    • (1986) Ark. Mat. , vol.24 , pp. 299-337
    • Triebel, H.1
  • 21
    • 26644433217 scopus 로고    scopus 로고
    • Approximate interpolation with applications to selecting smoothing parameters
    • Wendland H., and Rieger C. Approximate interpolation with applications to selecting smoothing parameters. Numer. Math. 101 (2005) 643-662
    • (2005) Numer. Math. , vol.101 , pp. 643-662
    • Wendland, H.1    Rieger, C.2
  • 22
    • 84966231566 scopus 로고
    • Strictly positive definite functions on spheres
    • Xu Y., and Cheney E.W. Strictly positive definite functions on spheres. Proc. Amer. Math. Soc. 116 (1992) 977-981
    • (1992) Proc. Amer. Math. Soc. , vol.116 , pp. 977-981
    • Xu, Y.1    Cheney, E.W.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.